Generating geometric surface



March 30, 1954 BRADNER 2,673,401

GENERATING GEOMETRIC SURFACE Filed Aug. 14, 1946 4 Sheets-Sheet lfiENTOR.

14 A4 ATTORNEYS.

March 30, 1954 BRADNER 2,673,401 GENERATING GEOMETRIC SURFACE Filed Aug.14, 1946 4 Sheets-Sheet 2 INVENTOR March 30, 1954 J. A. BRADNER2,673,401

GENERATING GEOMETRIC SURFACE Filed Aug. 14, 1946 4 Sheets-Sheet 3 IN VEN TOR.

March 30, 1954 BR 2,673,401 GENERATING GEOMETRIC SURFACE Filed Aug. 14,1946 4 Sheets-Sheet 4 i r 1' I+i= 4 L"=E s.l

| l J in I I l l l l I l i l a 2 A'B INVENTOR.

Patented Mar. 30, 1954 GENERATING GEOMETRIC SURFACE John A. Bradner,Shaker Heights, Ohio, to The Lees-Bradner Company,

assignor Cleveland,

Ohio, a corporation of Ohio Application August 14, 1946, Serial N 0.690,354 13 Claims. (Cl. 33-1795) This invention relates to surfaces.

An object of the invention is to provide an improved means foraccurately generating certain geometric surfaces.

Another object of the invention is to provide an improved means ofdescribing involute curves.

Another object of the invention is to provide an improved apparatuswhich will accurately describe involute curves from an infinite numberof base circles.

Another object of the invention is to provide an improved apparatuswhich may be easily and accurately adjusted to describe involute curvesfrom any of an infinite number of base circles.

Another object of the invention is to provide an improved apparatuswhich will generate involute curves from a single circular or arcuatemember and a single rectilinearly moving element.

Another object of the invention is to provide an improved apparatuswhich may be easily and economically manufactured.

Another object of the invention is to provide an improved apparatuswhich will be small and compact.

Another object of the invention is to provide an improved apparatuswhich will be easy to perate and read.

Another object of the invention is to provide an improved apparatuswhich will be composed of few and simple parts.

Another object of the invention is to provide an improved method ofgenerating involute curves.

Other objects will hereinafter appear.

The invention will be better understood from the description of onepractical embodiment generating geometric thereof, illustrated in theaccompanying drawings, in which:

Figure 1 is a diagrammatic view showing the relationship of variousinvolute curves to their respective base circles and lines and to eachother;

Figure 2 is a plan view of an apparatus for measuring the involute faceof gear teeth;

Figure 3 is a longitudinal section view of the apparatus taken on theline IIIIII of Figure 2; and

Figure 4 is a front elevational view of the apparatus of Figures 2 and3.

The involute now is one of the most popular forms for gear tooth design,because of the many and peculiar advantages possessed by this toothform, including the possibility of producing a tooth by a generativeaction. Numerous machines have been developed for generatively formingsuch teeth as by bobbing, grinding, and the like, and, as a basis forthis generative action, such devices have relied upon the base circle ofthe gear to be generated, using a master drum of precisely the diameterof this base circle, a master gear and rack having, the same basecircular diameter, or other equivalent mechanism to obtain thegenerative motion of the gear relative the tool.

This, of course, has necessitated the extremely accurate making of thebasic drum, master gear, or the like, and its associated parts, for eachbase circle diameter to which gear teeth are. to be generated, andlikewise has required the accurate adjustment of these parts whenever atool is changed to operate on a gear of a different base circlediameter.

The present invention contemplates the easy and rapid adjustment fromany base circle diameter to any other (within the range of theapparatus) without interchange of any parts whatsoever.

In the diagram of Figure 1, the center for a plurality of circles isindicated at O. R indicates the radius of a circular arc AB. The radiusof a smaller circular arc ab concentric therewith is indicated by r.

Assuming a line CD tangent to are AB at E, which line may roll withoutslipping upon the arc AB, point E of this line will trace the trueinvolute EF.

The lines C -D C D G -D and C -D all indicate successive positions ofthe line CD in rolling on the arc AB, and the points E E E and E arecorresponding positions of the point E along the involute EF.

R, R R R and R indicate the radii of the arc AB to the respective pointsof tangency of the lines C D C D O -D and C -D If now we consider theline cd, tangent to are ab at the intersection of this arc with radius R(and also radius r) it will be noted that line cd is parallel to lineCD, both being perpendicular to radius R.

Similarly line 0 -01 is parallel to C -D both being perpendicular toradii R T and so likewise c d 0 -12 and c d are parallel to C D C D andC D respectively, and the point e traces the involute ef, being thatdeveloped from base circle ab.

Similarly, any other line rolling on any other base circle with itscenter at 0 will trace the involute derived from this base circle; asfor instance the line Cg-Dg, rolling on the arc of circle Ag-Bg, whichis the base circle of the gear G shown as placed concentric with arcs aband AB. may have. a point Eg used to trace the involute gear tooth faceEgFg.

The only requirement is that the lines CgDg, ed and CD remain alwaysparallel, and that each remain at it fixed radiusv distance from center0.

If, now, instead of holding the circles stationary, we consider line CDas moving lengthwise and are AB as rotating about center so that thetangent portion of the line and are are moving at the same velocity, itwill be apparent that lines cd and Cg-Dg can also move lengthwise indirections parallel to line CD at rates such that the tangent portionsof these lines move at the same velocity as their respective arcs Ag-Bgab and the points e and Eg will trace the involutes ef and Eg-Fg.

The velocities of points Eg, e, E thus will be seen to be directlyproportional to the radii By, T and R, respectively.

If the motion of line CD is uniform, it will be apparent that the motionof lines cd and CgDg will also be uniform and proportional to theirrespective radial distances from point 0, and that the angularvelocities of points E, e and Ey will be identical.

Thus it is only necessary to make line CD move in a lengthwise directionand arc AB remain tangent to it and move, at the point of tangency, atthe same speed as line CD, and then to cause lines at (and/or Cg-Dg) tomove in a direction parallel to line CD at such a rate that points Eg, eand E all remain on the same radial line passing through center 0, toinsure all three of these points tracing their respective involutecurves; and when these conditions are met arcs Ag-Bg and ab may existonly as geometrical abstractions and need have no physical embodiment.

The apparatus shown in the remaining figures is based upon thisprinciple.

This apparatus is shown as a device for measuring the face of gearteeth. It consists of a base i, which is shown as a hollow castinghaving a depending front 2 and side 3 flanges and a top 4.

Extending vertically upward from the top 5 is a shaft or spindlefi, towhich is fixed a sector or arm 6 having arcuate end 6A6B, correspondingto the arc AB of the first figure.

Mounted in guideways 1 and 8, the former of which is formed in the uppersurface of top 6 and the latter of which is adjustably secured in placeby screws 9, is a transversely movable slide The projecting end of theshaft is formed into a square 24, to which may be applied a handle,knob, or wheel for rotating the shaft 23 to adjust the position of thecarriage on the base.-

The upper surface of bridge IE is provided with fixed guideways 25 andadjustable guideways 26, the latter of which is secured in position bymachine screws 21, and in these guideways is transversely movable slide28, having a straight inner edge 28c-28d, corresponding to either linecd or Cg-Dg of the first figure.

It will be understood that the guideways l and 8 are at all timesparallel to guideways 25 and 26, so that, irrespective of the adjustmentof screw 20, slides l0 and 28 must move parallel to each other.

Pivoted upon the shaft 5 is a hub 29, provided with an arm 30 having astraight side to the left (as shown in Figure 2) which lies in avertical plane including the axis of shaft 5.

Abutting this straight edge of the arm is an abutment, shown as a knifeedge 3!, fixed to slide In directly over line IBC-l GD.

A spring 32 presses the arm 30 against the abutment 3 I.

A similar abutment 33 projects upwardly from 7 carriage 28 directlyabove line 28c28d and likewise abuts the left hand edge of arm 33, whilea spring, similar to 32, is shown at 34, abutting the right hand edge ofthis bar and holding the knife edge tightly thereagainst.

Projecting upwardly from carriage 28 are two lugs 35, to which issecured, as by a bolt 33, an indicator 31, the contacting part 38 of thespindle of the indicator being so arranged as to be directly over theedge of abutment 33.

A gear G is shown as clamped on spindle shaft 5 by a nut 39 threaded onthe reduced end 4|] of the spindle.

In comparing the plan View of Figure 2 with the diagrammatic view ofFigure 1, it will be seen that the knife edge 3| is, in effect, thepoint I0 having a vertical flat surface IOC-IOD adjacent the arcuatesurface (SA-6B of a sector, this flat surface corresponding to line CDof the first figure.

To obviate any possibility of slippage between the end of sector 6 andthe slide 1 I], crossed tapes H and [2 of relatively unstretchablematerial, such as thin steel bands are provided, the ends of these beingsecured to the sector and slide as by machine screws I3. One end of tapeII is secured to the sector at 6A and its other end to the slide at HiD,while the ends of tape [2 are secured to the slide at IDC and to thesector at 6B. The top 4 of the base is formed with a large rectangularcentral opening, the side edges of which I l form, with the top andbottom of this base, guideways engaged by a bridgelike carriage havingvertical side portions l5 and a bridge or top It extending over thenarrower portion of sector 6.

The side portions of the carriage slide upon the upper surface of top 4,while on the bottom surface is a transverse plate or yoke l1, secured tothe side pieces 15 by machine screws l8.

The yoke has depending central boss l9 into which is threaded anadjusting screw 20, having a flange 2! lying against the front I of thebase and a collar 22 abutting the opposite side of this front and shownas held in place on the screw by tapered pin 23. l

E while the knife edge 33 and the overlying indicator contact 38 is, ineffect, the point e or Eg of Figure l.

The sector 6 rolls without slipping on slide l0,

' corresponding to are AB rolling on line CD, and

the point E (or 3|) traces the involute EF.

As it traces this involute, it causes line 280-2811 of slide 28 toreciprocate parallel to line MiG-48D at a rate which causes point 38 (orEg) to describe the involute Eg-Fg, so that the indicator generates atrue involute curve, the base circle of which is the distance from theaxis of shaft 5 to line 28c--28d.

The radius of this base circle, of course, may be easily varied byrotation of threaded shaft 20, to any one of the infinite radii possiblewithin the range of adjustment of the apparatus.

It will 'be seen that therelative linear velocity of line lGC-l0D isequal to the circumferential velocity of arc 6A-6B. In other words, ifwe let LV=the linear velocity of line IBC- 3D AV=the angular velocity ofarc 6A-6B R=the radius of arc 6A6B Lg=the linear velocity of line28c--2Bd rg=the radius of the base circle of gear G=the distance ofsurface 28c-28d from axis 0 erg-. 2 a *0 aerator While the mechanismshown and described is designed for the measuring of gear toothsurfaces, it will be apparent that, with little or no modification, itcan be used for the production of such surfaces.

For example, it is only necessary to substitute for the contact 38 ofthe indicator a cutting or forming tool, such as a shaper or millingcutter, a grinding wheel, lap, burnisher or the like and, of course, thetooth spacing of the gear may be arrived at by mounting any suitabledividing head or indexing mechanism upon or in the spindle 5.

While bands I I and I2 have been shown to preclude slippage between arc6A6B and straight surface IOClD, it will be obvious that with very lightloads, such as produced by the indicator shown, friction alone may besufiicient to cause these surfaces to roll upon each other withoutslipping.

While I have described the illustrated embodiment of my invention insome particularity, it will be apparent that many variations andmodifications thereof may be made by those skilled in the art, and Itherefore do not limit myself to the precise details herein shown anddescribed, but claim as my invention all variations, modifications andembodiments coming within the scope of the appended claims.

I claim:

1. A generating apparatus comprising two elements relatively movableabout an axis, two parallel elements carried by one of said firstmentioned elements and movable in guide means in parallel lines at fixeddistances from said axis, connections between the second of the twofirst mentioned elements and both parallel elements, said connectionsboth lying in the same plane including the axis.

2. A generating apparatus comprising two elements relatively movableabout an axis, two parallel elements carried by one of said firstmentioned elements and movable in guide means in parallel lines in aplane normal to the axis at fixed distances from said axis, connectionsbetween the second of the two first mentioned elements and both parallelelements, said connections both lying in the same plane including theaxis.

3. A curve generating device comprising two pivotally connectedsupports, article clamping means carried by one support, a movable toolholding means carried by the second support and movable in guide meansalong a line adjustably spaced from the axis of the pivot, a movablemember carried by said second mentioned support movable in guide meansalong a line parallel to the line of motion of the tool holding meansand at a, fixed distance from said axis, a connection between the firstmentioned support and the last mentioned linearly movable member causingsaid second mentioned linearly movable member to move at a constant ratein relation to the relative angular movement of the supports, aconnection between said first mentioned support and said tool carryingmember, both connections lying in a plane including the axis of thepivot.

4. A curve generating mechanism comprising a base, a holder pivotallymounted thereon, parallel guide-ways carried by the base at difierentdistances from the pivotal axis of the holder, slides in saidguide-ways, a driving member connected to the holder and having positiverolling contact with one of the slides, a member-pivotally mountedco-axial to said holder and having 6 positive driving connectionsbetween fixed points on each of said slides, said fixed points lying ina plane including the pivotal axis.

5. A curve generating mechanism comprising a base, a holder pivotallymounted thereon, parallel guide-ways carried by the base at differentdistances from the pivotal axis of the holder, one of said guide-waysbeing adjustable toward and from the pivotal axis, slides in saidguide-ways, a driving member connected to the holder and having positiverolling contact with one of the slides, a member pivotally mounted torotate about the same axis as said holder and having positive drivingconnections between fixed points on each of said slides, said fixedpoints lying in a plane including the pivotal axis.

6. A curve generating apparatus comprising a base, a vertical spindlemounted thereon, parallel horizontal guideways carried by the base,slides movable in said guideways, an extension on said spindle having anarcuate end in driving engagement with one of said slides, an armpivoted on said spindle, and connections between said arm and both saidslides, said connections lying in a single plane including the axis ofthe spindle.

7. A curve generating apparatus comprising a base, a vertical holderspindle mounted thereon, two parallel horizontal guideways carried bythe base, slides movable in both said guideways, an extension on saidspindle having an arcuate end in driving engagement with one of saidslides, an arm pivoted on said spindle, and connections between said armand both said slides, said connections lying in a single plane includingthe axis of the spindle.

8. A curve generating apparatus comprising a base, a vertical holderspindle mounted thereon, horizontal guideways carried by the base, acarriage movable upon said base, guideways on the carriage parallel tothe guideways on the base, slide movable in both said guideways, an eX-tension on said spindle having an arcuate end in driving engagement withone of said slides,

. an arm pivoted on said spindle, and connections between said arm andboth said slides, said connections lying in a single plane including theaxis of the spindle.

9. A curve generating apparatus comprising a base, a vertical holderspindle mounted thereon, horizontal guideways carried by the base, acarriage movable upon said base and adjustable toward and from saidspindle, guideways on the carriage parallel to the guideways on thebase, a slide movable in said guideways on the base, a second slidemovable in the guideways on the carriage, an extension on said spindlehaving an arcuate end in driving engagement with one of said slides, anarm pivoted on said spindle, and connections between said arm and bothsaid slides, said connections lying in a single plane including the axisof the spindle.

10. A curve generating device comprising, a base, a vertical spindlepivotally mounted thereon, a horizontal guideway on said base, a slidemovable along said guideway, horizontal guideways on the base angularlydisposed with respect to said first mentioned guideway, a carriagemovable along said second mentioned guideways, moving means for movingsaid carriage along said guideways, guideways carried by said carriageparallel to the first mentioned guideways on the base, a slide movablein said guideways on the carriage, an arm fixed to said spindle andhaving an arcuate end in driving engagement With the first mentionedslide, an arm pivotally mounted on said spindle and having positivedriving connections with both said slides, both driving connectionslying in the same radial plane including the axis of the spindle, a toolconnected to said second mentioned slide and clamping means for clampingan article to said spindle.

11. A curve generating device comprising a base, a vertical spindlepivotally mounted thereon, a horizontal guideway on said base extendingalong a line spaced from the spindle, a slide movable along saidguideway, horizontal guideways on the base angularly disposed withrespect to said first mentioned guideway, a carriage movable along saidsecond mentioned guideways, moving means for moving said carriage alongsaid guideways, guideways on said carriage parallel to the firstmentioned guideways on the base, a second slide movable in saidguideways on the carriage, an arm fixed to said spindle and having anarcuate end in driving engagement with the first mentioned slide, an armpivotally mounted on said spindle and having positive drivingconnections with both said slides, both driving connections lying in thesame radial plane including the axis of the spindle, a tool connected tosaid second mentioned slide and clamping means for clamping an articleto said spindle.

12. A curve generating device comprising a base, a vertical spindlepivotally mounted thereon, a horizontal guideway on said base extendingalong a line spaced from the spindle, a slide movable along saidguideway, horizontal guideways on the base angularly disposed withrespect to said first mentioned guideway, a carriage movable along saidsecond mentioned guideways, a, lead screw for moving said carriage alongsaid guideways, guideways on said carriage parallel to the firstmentioned guideways on the base, a second slide movable in saidguideways on the carriage, an arm fixed to said spindle and having anarcuate end in driving engagement with the first mentioned slide, an armpivotally mounted on said spindle and having positive drivingconnections with both said slides, both driving connections lying in thesame radial plane including the axis of the spindle, a tool connected tosaid second mentioned slide and clamping means for clamping an articleto said spindle.

13. A curve generating device comprising a base, a vertical spindlepivotally mounted thereon, a horizontal guideway on said base, a slidemovable along said guideway, horizontal guide- Ways on the baseangularly disposed with respect to said first mentioned guideway, acarriage movable along said second mentioned guideways, moving means formoving said carriage along said guideways, guideways on said carriageparallel to the first mentioned guideways on the base, a second slidemovable in said guideways on the carriage, an arm fixed to said spindleand having an arcuate end in driving engagement with the first mentionedslide, an arm pivotally mount-v ed on said spindle, rigid radiallydisposed abutments between one side of said arm and both said slides,the contacting sides of said abutments lying in the same plane includingthe axis of the spindle, resilient means maintaining the contact withsaid abutments, a tool connected to said second mentioned slide, andclamping means for clamping an article to said spindle.

J. A. BRADNER.

References Cited in the file of this patent UNITED STATES PATENTS NumberName Date 1,564,589 Laessker Dec. 8, 1925 2,013,365 Snarry Sept. 3, 19352,176,924 Olson Oct. 24, 1939 FOREIGN PATENTS Number Country Date637,563 Germany Oct. 30, 1936 OTHER REFERENCES Involute Gears, W.Steeds, Longmans, Green and Co., 1948, pages 103 and 104. (Copy in Sci,-entific Library.)

